It has previously been proposed--see German Democratic Republic Pat. No. 104 259--to provide an ink roller train in which a metering roller is included which is constructed as a plurality of axially spaced disks. The disks are, selectively, engaged with an ink supply roller and an ink receiving roller. It has been found that the arrangement there disclosed has a disadvantage, namely that the disks, during their engagement with the ink ink supply roller, are not available for milling of the ink film on the downstream ink-receiving roller and, further, that, upon selective engagement, cyclic acceleration and braking of the rollers occurs which, in addition to the shocks of impingement as the disks impinge on the ink-receiving roller, cause disturbances within the ink train and, specifically, within the drive gearing of the rollers of the ink train. These disturbances can be transferred to the printing cylinders, for example to the plate cylinder, and detrimentally affect the eventual printing result due to interference with continuous and desired supply of ink.